polynomial-math

In my code i need to calculate CRC-16 16 bit values for the HEX values stored as NSdata, below is the code snippet to calculate CRC-16 in c. void UpdateCRC(unsigned short int *CRC, unsigned char x) { // This function uses the initial CRC value passed in the first // argument, then modifies it using the single character passed // as the second argument, according to a CRC-16 polynomial // Arguments: // CRC -- pointer to starting CRC value // x -- new character to be processed // Returns: // The function does not return any values, but updates the variable // pointed to by CRC static int const

I need to calculate coefficients of polynomial using Lagrange interpolation polynomial , as my homework, I decide to do this in Javascript. here is definition of Lagrange polynomial (L(x)) Lagrange basis polynomials are defined as follows Calculate y value for specific X (W(x) function) is simple but I need to calculate coefficients of polynomial (array of [a0, a1, ..., an]) I need to do this to n<=10 but it will be nice to have arbitrary n, then I can put that function into horner function and draw that polynomial. I have function that calculate denominator in first equation function

I have 1x1024 matrix. So I'd like to estimate a polynomial equation. X= (0:1023)' Y= acquired data. A 1024 element vector Then I try this in MATLAB: polyfit(x,y,5) But MATLAB makes an abnormal result with warning. Warning: Polynomial is badly conditioned. Add points with distinct X values, reduce the degree of the ... I don't understand what am I doing wrong? Update I got a bunch of numbers like this. Y= -0.0000000150 ... 0.00001 ... 0 ... 0.17 X= 0~255 polyfit(X,Y,4) I got a polynomial but it does not match to original curve. Is there any options to match between original curve and polyfit's

Horner's rule is used to simplify the process of evaluating a polynomial at specific variable values. https://rosettacode.org/wiki/Horner%27s_rule_for_polynomial_evaluation#Standard_ML I've easily applied the method using SML, to a one variable polynomial, represented as an int list: fun horner coeffList x = foldr (fn (a, b) => a + b * x) (0.0) coeffList This works fine. We can then call it using: - val test = horner [1.0, 2.0, 3.0] 2.0; > val test = 17.0 : real Where [1.0, 2.0, 3.0] is the list representing the polynomial coefficients, 2.0 is the value of the variable x, and 17.0 is the

Can I solve a system of nonlinear equations in terms of parameters in python? Is there a example or tutorial? I can do this easily in maple, but the expressions for my particular system are pretty big and copying them over is quite hard. Example: sigma*(y-x) = 0 x*(rho-z)-y = 0 x*y-beta*z = 0 You should get the solutions: [[x = 0, y = 0, z = 0], [x = sqrt(beta*rho-beta), y = sqrt(beta*rho-beta), z = rho-1], [x = -sqrt(beta*rho-beta), y = -sqrt(beta*rho-beta), z = rho-1]] The reason I ask: I have a large system of nonlinear ODEs. I want to solve for the fixed points (this is doable, it's been

I was trying to solve a linear system Xc=y that was square. The methods I know to solve this are: using inverse c=<X^-1,y> using Gaussian elimination using the pseudo-inverse It seems as far as I can tell that these don't match what I thought would be the ground truth. First generate the truth parameters by fitting a polynomial of degree 30 to a cosine with frequency 5. So I have y_truth = X*c_truth . Then I check if the above three methods match the truth I tried it but the methods don't seem to match and I don't see why that should be the case. I produced fully runnable reproducible code:

I am attempting to read in data and plot them on to a graph using python (standard line graph). Can someone please advise on how I can classify whether certain points in a graph are uptrends or downtrends programmatically? Which would be the most optimal way to achieve this? Surely this is a solved problem and a mathematical equation exists to identify this? here is some sample data with some up trends and downtrends x = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30] y = [2,5,7,9,10,13,16,18,21,22,21,20,19,18,17,14,10,9,7,5,7,9,10,12,13,15,16,17,22,27]